In 2004, two R/C residential buildings were retrofitted by using a hybrid base isolation system in Solarino, Sicily, and subsequently five free vibration tests were carried out in one of these buildings. The hybrid base isolation system combined high damping rubber bearings with low friction sliders. In terms of numerical modeling, a single-degree-of-freedom system is developed here with a new five-parameter trilinear hysteretic model for the simulation of the high damping rubber bearing, coupled with a Coulomb friction model for the simulation of the low friction slider. Furthermore, a shear beam type, four-degree-of-freedom model is used to numerically simulate the superstructure. Next, experimentally obtained data from the five initial-displacement, free vibration tests were used for the calibration of this six-parameter model describing the base isolation system. Following up on the model development, the present study employs Monte-Carlo simulations in order to investigate the effect of the unavoidable variation in the values of the six-parameter mechanical model on the response of both the hybrid base isolation system and the superstructure comprising the Solarino building. The calibrated parameters values from all the experiments are used as mean values, while the standard deviation for each parameter is deduced from the identification tests employing best-fit optimization for each experiment separately. The results of the Monte-Carlo simulations show that variation in the material parameters of the base isolation system produce a nonstationary effect in the response, which can be traced by the time evolution of its mean and standard deviation as computed from the response at different time instants. In addition, there is a magnification effect, since the coefficient of variation of the response, for most of the parameters, is larger than the coefficient of variation in the parameter values. The high level of nonlinearity in the base isolation system, as observed in the amplitude of vibration brought about by large initial displacements, helps explain the previously mentioned effects.